• The Transactions of the Korean Institute of Electrical Engineers
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• v.40 no.7
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• pp.690-695
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• 1991

The ability to linearize a nonlinear system by feedback and coordinate change reduces to finding an integrating factor for a one-form which is determined from the system dynamics. Utilizing Taylor series expansion of this one-form, we characterize approximate linearizabilitu. A constructive method is derived for approximate linearization up to order 2.

• International Journal of Internet, Broadcasting and Communication
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• v.6 no.2
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• pp.1-9
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• 2014

This paper presents a study on nonlinear time varying systems based on differential geometry. A brief introduction about controllability and involutivity will be presented. As an example, the exact feedback linearization and the approximate feedback linearization are used in order to show some application examples.

• Proceedings of the IEEK Conference
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• 2003.07c
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• pp.2863-2866
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• 2003

In nonlinear control fields, for irregular nonlinear systems, control form which consists of approximate tracking control law and exact tracking control law and which switches between two laws has been proposed recently. In this thesis, we design new switching control law which connect approximate linearization control law and exact linearization control law by fuzzy rules for irregular nonlinear system, ball and beam system. Fuzzy switching controller designed by fuzzy concept is proved that designed scheme overcomes singularities of irregular system, improves unstability problem of switching procedure, and has more efficient control value through simulation. Stability of fuzzy control system proved by Lyapunov's stability theorems.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.5
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• pp.819-832
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• 2017

We propose a new switching control scheme for a ball and beam system by utilizing two linearization methods. First, the Jacobian linearization is applied and state observer is developed afterward. Then, motivated [6], the approximate input-output linearization is carried out, and after that, the Jacobian linearization is applied along with the design of state observer. Since the second approach requires two linearizations, it is called a two-step linearization method. The state observer is needed for the estimation of the velocities of ball and motor movement. Since the Jacobian linearization based controller tends to provide faster response at the initial time, and after that, the two-step linearization based controller tends to provide better response in terms of output overshoot and convergence to the origin, it is natural to give a switching control scheme to provide the best overall control response. The validity of our control scheme is shown in both simulation and experimental results.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1249-1262
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• 2010

An approximate alternating linearization decomposition method, for minimizing the sum of two convex functions with some separable structures, is presented in this paper. It can be viewed as an extension of the method with exact solutions proposed by Kiwiel, Rosa and Ruszczynski(1999). In this paper we use inexact optimal solutions instead of the exact ones that are not easily computed to construct the linear models and get the inexact solutions of both subproblems, and also we prove that the inexact optimal solution tends to proximal point, i.e., the inexact optimal solution tends to optimal solution.

• International Journal of Control, Automation, and Systems
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• v.2 no.2
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• pp.156-164
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• 2004

The unmanned tandem helicopter, which is a MIMO nonlinear system with complexity and inherent instability, exists in unstable zero dynamics. In this paper, approximate linearization is presented to design the controller for output tracking of an unmanned tandem helicopter based on the dynamic augment method, and the simulation results are encouraging.

• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.139-149
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• 2018

Many practical engineering problems are associated with nonlinear systems subjected to nonstationary random excitations. Equivalent linearization methods are commonly used to seek for approximate solutions to this kind of problems. Compared to various approaches developed in the frequency and mixed time-frequency domains, though directly solving the system equation of motion in the time domain would improve computation efficiency, only limited studies are available. Considering the fact that the orthogonal functions have been widely used to effectively improve the accuracy of the approximated responses and reduce the computational cost in various engineering applications, an orthogonal-function-based equivalent linearization method in the time domain has been proposed in the current paper for nonlinear systems subjected to nonstationary random excitations. In the numerical examples, the proposed approach is applied to a SDOF system with a set-up spring and a SDOF Duffing oscillator subjected to stationary and nonstationary excitations. In addition, its applicability to nonlinear MDOF systems is examined by a 3DOF Duffing system subjected to nonstationary excitation. Results show that the proposed method can accurately predict the nonlinear system response and the formulation of the proposed approach allows it to be capable of handling any general type of nonstationary random excitations, such as the seismic load.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.3
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• pp.372-384
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• 1993

The inverted pendulum system has interesting and challenging problems related to robotics and rocket attitude control view of both control theory and applications. Generally approximately linearized plant models are employed to control the system. In this paper a recently developed control theory based on differentiable manifold theory is used to control the inverted pendulum system which is typically nonlinear. First, the nonlinear model is transformed into the approximate feedback linearized system by nonlinear state feedback. Secondly, the linear controller is designed using the pole-placement method for the approximate feedback linearized plant model, the output of which are finally inverse-transformed to yield the control input to the actual system of the inverted pendulum. The proposed method is evaluated by the computer simulation to compare with the 3rd order linearization model.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.9
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• pp.109-121
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• 2000

A simplified modeling approach of free vibration for occupied car seats was demonstrated to be feasible. The model consisting of interconnected masses springs and dampers was initially broken down into subsystems and experiments conducted to determine approximate values for model parameters. Which were each stiffness and damping value. Nonlinear equations of motion were derived and model parameters obtained in experiments were applied to these equations. A mathematical model of free vibration for car seat and mannequin system was built with 7 degrees of freedom. in order to calculate natural frequencies and the corresponding mode shapes. linear equations of motion were obtained through linearization. In order to explore the effects of each model parameter free vibration analysis were preformed.